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Rational and Irrational Numbers/Transcript
Transcript Title text reads, The Mysteries of Life with Tim and Moby. A boy, Tim, is playing with a Moby robot action figure and a toy dinosaur. TIM: Beep beep beep! Beep beep! Raaa! Beep beep beep! Beep beep! Moby appears in the doorway. He beeps and looks at Tim with a worried expression. TIM: I wasn’t…um, it's for school. On-screen, a letter appears. Text reads as Tim narrates: Dear Tim and Moby, What’s the deal with rational numbers? Are there irrational numbers too? From, Gil TIM: Well, a rational number is any number that can be written in fraction form. A label appears, reading, rational number. TIM: Like three-thirds, five-eighths, one-half or nine-tenths. On-screen, the following rational numbers appear: three-thirds, five-eighths, one-half, and nine-tenths. TIM: Mathematics organizes numbers into different sets. Whole numbers are positive numbers without decimals. On-screen, a circle appears, labeled, whole numbers. The whole numbers 0, 1, 2, 3, 22, and 751 appear within the circle. TIM: Whole numbers also include any fractions that represent a whole number, like, say, twenty-fifths. On-screen, an equation reads, twenty-fifths equals 4. The fraction, twenty-fifths, appears within the whole numbers circle. TIM: The integers group includes both whole numbers and their negatives. On-screen, a bigger circle labeled, integers, surrounds the whole numbers circle. 4 integers appear inside the larger circle, but outside the smaller circle. They are: negative 233, negative 64, negative 14, and negative 1. TIM: As you can see from this diagram, whole numbers are included in the set of all integers. On-screen, an arrow points to the whole numbers circle within the integers circle. TIM: Rational numbers are any number that can be expressed as a over b, where both a and b, are integers, and b does not equal 0. On-screen, a third, even bigger circle surrounds the integers circle and the whole numbers circle. It is labeled, rational numbers. Within the largest circle, but outside the smaller circles, the following rational numbers appear: three-fifths, negative seven-twenty-fifths, one-half, and one-third. The fraction, a, over b, appears in the background. TIM: Decimals can be rational too. As long as a decimal is either terminating or repeating, it is a rational number. Moby beeps. TIM: Terminating just means that the decimal comes to an end, like, say 7.892. On-screen, the number 7.892 appears. TIM: A repeating decimal is one that goes on forever. Like one-third, which, as a decimal, is 0.33333333, and so on to infinity. On-screen, the fraction one-third appears. A decimal scrolls by, reading 0.3333, with the 3s repeating to infinity. TIM: So one-third goes on forever, but since it's predictable, it's a rational number. On-screen, the fraction, one-third, appears inside the rational numbers circle. TIM: Decimals that don’t repeat and don’t end are called irrational numbers. On-screen, a new circle appears, separate from the other three circles. It’s labeled, irrational numbers. TIM: You’ve probably heard of pi. A label appears, reading, pi. The Greek letter, pi, appears next to it. TIM: Pi is often rounded to twenty-two-sevenths or 3.14, but in reality, those are just approximations. On-screen, a fraction appears, reading, twenty-two-sevenths. Next to it, the decimal, 3.14, appears. TIM: Pi is 3.1415926535… And so on. On-screen, dozens of digits are added to the end of 3.14. TIM: It keeps going on like that, never repeating, and never ending. Pi is an irrational number. At least theoretically, pi can be written as a decimal, but not a fraction. On-screen, the irrational numbers circle appears, and the Greek letter pi appears within it. Moby beeps. TIM: The term rational contains the word ratio; and a ratio is the same as a fraction, so that can help you remember what a rational number is! On-screen, the rational numbers circle appears, surrounding the integers circle and the whole numbers circle. The word, ratio, is highlighted within the word, rational. TIM: That’s any number that can be written as a fraction. There you go. Moby beeps. He pulls out a female doll in a polka dot dress, and points to Tim's Moby toy. TIM: Oh…Okay. On-screen, Moby's hand holds the Moby doll, and Tim's hand holds the doll in the polka dot dress. Moby beeps, moving his doll up and down. Tim answers in a high-pitched voice, moving his doll up and down: TIM: Why sure, I'd love to go the movies with you. Can Mister Dinosaur come too? On-screen, Tim moves the dinosaur in between the Moby doll and the girl doll. Moby pulls his doll away and beeps at Tim. TIM: What do you mean? I'm not getting carried away.Category:BrainPOP Transcripts